During the operation and service of a ship, its power system will affect the stability, reliability, and safety of the ship’s power system and the ship’s vitality if there are typical problems, such as unstable operation and vibration of the shaft system. If the tail bearing is not properly installed, it will lead to increased vibration at its support during operation, which will cause the propulsion system components to come loose and even produce destructive accidents. This paper combines the theory of multi-degree-of-freedom system dynamics to study the propulsion system vibration modeling technology based on the bearing–mounting error, analyze the mapping law between the bearing–mounting error and the shaft system vibration, construct a shaft system vibration model with the bearing–mounting error included, and analyze the influence of the bearing vertical mounting error and lateral mounting error on the vibration performance of the shaft system. This paper establishes the equations of motion of the shaft system with bearing–mounting errors and analyzes the relationship between the bearing vertical mounting errors and lateral mounting errors and the amplitude, speed, and acceleration of the paddle shaft system. The analyzed results show that the vibration response of the shaft system gradually increases with the increase in the bearing–mounting error. With the increase in the bearing vertical mounting error, the increase in vibration amplitude and the transient response of vibration acceleration in the vertical direction is larger than that in the horizontal direction, and the sensitivity of the transient response of vibration acceleration in the vertical direction to the bearing vertical mounting error is larger than that in the horizontal direction. With the increase in the bearing lateral mounting error, the increase in the vibration acceleration transient response value of the paddle shaft system in the horizontal direction is larger than that in the vertical direction, and the sensitivity of the vibration amplitude and vibration acceleration transient response to the bearing lateral mounting error in the horizontal direction is larger than that in the vertical direction. The bearing vertical installation error has a greater effect on the vibration of the paddle shaft system in the vertical direction than in the horizontal direction, and the bearing lateral installation error has a greater effect on the vibration of the paddle shaft system in the horizontal direction than in the vertical direction. The results of this paper can provide a theoretical basis and technical reference for the installation and calibration of ship propulsion system.

In industrial environments such as ports and warehouses, autonomous logistics vehicles face significant challenges in coordinating multiple vehicles while ensuring safe and efficient path planning. This study proposes a novel real-time cooperative control framework for autonomous vehicles, combining reinforcement learning (RL) and distributed model predictive control (DMPC). The RL agent dynamically adjusts the optimization weights of the DMPC to adapt to the vehicle’s real-time environment, while the DMPC enables decentralized path planning and collision avoidance. The system leverages multi-source sensor fusion, including GNSS, UWB, IMU, LiDAR, and stereo cameras, to provide accurate state estimations of vehicles. Simulation results demonstrate that the proposed RL-DMPC approach outperforms traditional centralized control strategies in terms of tracking accuracy, collision avoidance, and safety margins. Furthermore, the proposed method significantly improves control smoothness compared to rule-based strategies. This framework is particularly effective in dynamic and constrained industrial settings, offering a robust solution for multi-vehicle coordination with minimal communication delays. The study highlights the potential of combining RL with DMPC to achieve real-time, scalable, and adaptive solutions for autonomous logistics.

Local installation errors in stern-tube bearings can substantially affect shaft alignment, yet conventional calculations often represent these errors only as nominal support displacements. This study extends the three-moment-equation framework by explicitly parameterising vertical and lateral offsets of the aft stern bearing within the compatibility equations for a multi-supported shaft beam. The method is benchmarked against published bearing-elevation data. Relative to the reference calculation, the mean absolute error (MAE) and root-mean-square error (RMSE) are 0.043 and 0.055 mm, respectively; relative to the reported installation elevations, the corresponding values are 0.229 and 0.281 mm. The method is then applied to the shafting system of a large container ship to evaluate changes in shaft deformation and slope, bearing clearance, maximum pressure, bearing load, shear force, bending moment, and support stiffness. For this case, the vertical offset is the dominant disturbance: an increase from 0 to 0.1 mm raises the maximum aft-bearing pressure by 12.19% and reduces its support stiffness by 14.39%. The effects of lateral offset remain limited up to 0.3 mm, whereas a secondary contact region develops at approximately 0.4 mm. This transition is case-specific and should not be interpreted as a universal tolerance limit. The method is intended as a rapid preventive tool for assessing installation tolerances; however, its pressure and stiffness predictions require further validation of the contact model and additional experimental evidence.